The stability of the block θ-methods

DOI10.1093/imanum/13.1.101zbMath0764.65039OpenAlexW2073857818MaRDI QIDQ4024989

Lianhua Lu

Publication date: 22 February 1993

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/13.1.101

zbMATH Keywords

performancecomparisonstabilitydelay differential equationsmultistep methodorder of accuracysingly-implicit Runge-Kutta methodblock theta-method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) General theory of functional-differential equations (34K05)

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The asymptotic stability of one-parameter methods for neutral differential equations ⋮ The convergence of two Newton-like methods for solving block nonlinear equations and a class of \(r\)-point \((r+1)\)st-order \(A\)-stable one-block methods ⋮ Functionally-fitted block \( \theta \)-methods for ordinary differential equations ⋮ Continuous block implicit hybrid one-step methods for ordinary and delay differential equations ⋮ Parallel step-by-step methods ⋮ Stability of implicit one-block methods for delay differential equations ⋮ Stability estimates of difference schemes for neutral delay differential equations ⋮ Meshless techniques for convection dominated problems ⋮ Functionally-fitted block methods for ordinary differential equations ⋮ Asymptotic stability of general linear methods for systems of linear neutral delay differential-algebraic equations

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